Theory of Raman scattering from Leggett's collective mode in a multiband superconductor: Application to MgB${}_2$

Abstract

In 1966 Leggett used a two-band superconductor to show that a new collective mode could exist at low temperatures, corresponding to a counter-flow of the superconducting condensates in each band. Here, the theory of electronic Raman scattering in a superconductor by Klein and Dierker (1984) is extended to a multiband superconductor. Raman scattering creates particle/hole pairs. In the relevant $A_{1g}$\ symmetry, the attraction that produces pairing necessarily couples excitations of superconducting pairs to these p/h excitations. In the Appendix it is shown that for zero wave vector transfer this coupling modifies the Raman response and makes the long-range Coulomb correction null. The 2-band result is applied to MgB${}_2$ where this coupling activates Leggett's collective mode. His simple limiting case is obtained when the interband attractive potential is decreased to a value well below that given by LDA theory. The peak from Leggett's mode is studied as the potential is increased through the theoretical value: With realistic MgB${}_2$\ parameters, the peak broadens through decay into the continuum above the smaller ($\pi$ band) superconducting gap. Finite $q$ effects are also taken into account, yielding a Raman peak that agrees well in energy with the experimental result by Blumberg \textit{et el.} (2007). This approach is also applied to the $q=0$, 2-band model of the Fe-pnictides considered by Chubukov \textit{et al.}(2009).

arXiv comment10 pages, 3 figures. To appear in Physical Review B

References in corpus (9)

• Beyond Eliashberg superconductivity in MgB2: anharmonicity, two-phonon scattering, and multiple gaps
• Evidence for two superconducting energy gaps in MgB2 by point-contact spectroscopy
• Two-Band Superconductivity in MgB2
• Direct evidence for a multiple superconducting gap in MgB2 from high-resolution photoemission spectroscopy
• Phonon dispersion and lifetimes in MgB2
• Observation of Leggett's collective mode in a multi-band MgB2 superconductor
• The two colors of MgB2
• Theory of Raman response in a superconductor with extended s-wave symmetry: Application to Fe-pnictides
• Anharmonicity and self-energy effects of the E2g phonon in MgB2

Cited by in corpus (25)

• Critical Quadrupole Fluctuations and Collective Modes in Iron Pnictide Superconductors
• Nonlinear optical response of collective modes in multiband superconductors assisted by nonmagnetic impurities
• Leggett modes in iron-based superconductors as a probe of Time Reversal Symmetry Breaking
• Topological superconducting phases from inversion symmetry breaking order in spin-orbit-coupled systems
• Theory of light-induced resonances with collective Higgs and Leggett modes in multiband superconductors
• Signature of the Leggett mode in the A1g Raman response: from MgB2 to iron-based superconductors
• Pinpointing Gap Minima in Ba(Fe${}_{0.94}$Co${}_{0.06}{)}_2$As${}_2$ \textit{via} Band Structure Calculations and Electronic Raman Scattering
• A balancing act: Evidence for a strong subdominant d-wave pairing channel in $\mathrm{B}{\mathrm{a}}_{0.6}{\mathrm{K}}_{0.4}\mathrm{F}{\mathrm{e}}_2\mathrm{A}{\mathrm{s}}_2$
• Ground state, collective mode, phase soliton and vortex in multiband superconductors
• Collective modes in multiband superfluids and superconductors: Multiple dynamical classes
• Conservation laws, vertex corrections, and screening in Raman spectroscopy
• Superconductivity and electronic fluctuations in Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ studied by Raman scattering
• Strong interaction between electrons and collective excitations in multiband superconductor MgB2
• High Tc superconductivity in CaKFe${}_4$As${}_4$ in absence of nematic fluctuations
• Raman response in the nematic phase of FeSe
• Raman Study of Cooper Pairing Instabilities in (Li${}_{1-x}$Fe${}_x$)OHFeSe
• Multi-Dimensional Coherent Spectroscopy of Light-Driven States and their Collective Modes in Multi-Band Superconductors
• Leggett Modes in Dirac Semimetals
• Many-body physics-induced selection rules: application to Raman spectroscopy
• Spin-orbit interaction enabled electronic Raman scattering from charge collective modes
• Linear spectroscopy of collective modes and the gap structure in two-dimensional superconductors
• Amplitude mode in a multi-gap superconductor MgB${}_2$ investigated by terahertz two-dimensional coherent spectroscopy
• Electronic Raman response of a superconductor across a time reversal symmetry breaking phase transition
• Superconductivity with repulsion: a variational approach
• Raman response of collective modes in multicomponent superconductors